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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sat, 29 Mar 2025 13:54:22 -0500
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On 3/29/2025 4:19 AM, joes wrote:
> Am Fri, 28 Mar 2025 17:38:22 -0500 schrieb olcott:
>> On 3/28/2025 5:30 PM, dbush wrote:
>>> On 3/28/2025 6:09 PM, olcott wrote:
>>>> On 3/28/2025 3:38 PM, dbush wrote:
>>>>> On 3/28/2025 4:30 PM, olcott wrote:
>>>>>> On 3/28/2025 2:24 PM, dbush wrote:
>>>>>>> On 3/28/2025 3:21 PM, olcott wrote:
>>>>>>>> On 3/28/2025 4:43 AM, Fred. Zwarts wrote:
>>>>>>>>> Op 28.mrt.2025 om 03:13 schreef olcott:
>>>>>>>>>> On 3/27/2025 9:04 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/27/25 9:07 PM, olcott wrote:
>>>>>>>>>>>> On 3/27/2025 7:38 PM, dbush wrote:
>>>>>>>>>>>>> On 3/27/2025 8:34 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/27/2025 7:12 PM, dbush wrote:
> 
>>>>>>>>>>>> TM's cannot possibly ever report on the behavior of the direct
>>>>>>>>>>>> execution of another TM. I proved this many times in may ways.
>>>>>>>>>>>> Ignoring these proofs IT NOT ANY FORM OF REBUTTAL.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>> Sure they can.
>>>>>>>>>>> WHere is your proof? And what actual accepted principles is is
>>>>>>>>>>> based on?
>>>>>>>>>>>
>>>>>>>>>> No TM can take another directly executed TM as an input and
>>>>>>>>>> Turing computable functions only compute the mapping from inputs
>>>>>>>>>> to outputs.
>>>>>>>>>>
>>>>>>>>> If A TM can only compute the mapping from *its* input to *its*
>>>>>>>>> output, it cannot be wrong.
>>>>>>>>
>>>>>>>> Taking a wild guess does not count as computing the mapping.
>>>>>>>
>>>>>>> False.  The only requirement is to map a member of the input domain
>>>>>>> to a member of the output domain as per the requirements.
>>>>>>> If it does so in all cases, the mapping is computed.  It doesn't
>>>>>>> matter how it's done.
>>>>>>>
>>>>>> Unless an input is transformed into an output on the basis of a
>>>>>> syntactic or semantic property of this input it is not a Turing
>>>>>> computable function.
>>>>>> int StringLength(char *S)
>>>>>> {
>>>>>>     return 5;
>>>>>> }
>>>>>> Does not compute the string length of any string.
>>>>>>
>>>>> False.  It computes the length of all strings of length 5.
>>>>
>>>> It does not compute (a sequence of steps of an algorithm that derive
>>>> an output on the basis of an input) jack shit it makes a guess.

> Even a constant function is a "computation", even if it doesn't actually
> do any work.
> 

That is not transforming an input finite string
into its corresponding output finite string.

Historically this is a decider:

void X(char* S)
{
   return;
}

It "accepts" all finite string inputs.

>>> Doesn't matter. If the requirement is to return 5 for strings that have
>>> a length of 5, it meets the requirement.
>>
>> The actual requirement is to compute the mapping from a finite string to
>> its length using a sequence of algorithmic steps.
>> Likewise for halting. Compute the mapping from a finite string of
>> machine code to the behavior that this finite string specifies.
> Do you reckon the direct execution of a TM contradicts the specification?
> 


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer